An apparatus and method detects an open condition of a grounding path provided by a rotor grounding brush electrically connecting a rotor body of a rotor to electrical ground. The rotor includes an insulated field winding wrapped around the rotor body and is configured to generate a magnetic field upon receipt of an exciter voltage across lower and upper extremities of the insulated field winding. The method includes applying a square wave voltage signal to a second end of each of a first and a second buffer resistor, where a first end of each of the buffer resistors is operatively connected to respective upper and lower leads of the exciter voltage source, and calculating the total capacitance between the insulated field winding and electrical ground. The total capacitance when compared to a pre-selected capacitance value is determinative of the absence of the grounding path.
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15. A method for detecting an open condition of a grounding path provided by a rotor grounding brush electrically connecting an electrically conductive body of a rotor to electrical ground, the rotor including an insulated field winding wrapped around the electrically conductive body and coupled to receive an exciter voltage at first and second exciter nodes, the method comprising:
applying a periodic oscillating voltage signal to a common node between first and second buffer resistors;
coupling the exciter voltage to the first and second buffer resistors;
calculating a total capacitance between the insulated field winding and electrical ground; and
detecting the open condition of the grounding path based on the total capacitance.
28. A computer readable storage medium having program code recorded thereon for detecting an open condition of a grounding path provided by a rotor grounding brush electrically connecting an electrically conductive body of a rotor to electrical ground, the rotor including an insulated field winding wrapped around the electrically conductive body and connected to receive an exciter voltage at first and second exciter nodes, comprising;
a first program code encoded in computer-readable storage media for applying a periodic oscillating voltage signal to a common node between first and second buffer resistors;
a second program code encoded in computer-readable storage media for coupling the exciter voltage to the first and second buffer resistors;
a third program code encoded in computer-readable storage media for calculating a total capacitance between the insulated field winding and electrical ground; and
a fourth program code encoded in computer-readable storage media for determining from the total capacitance whether an open condition exists in the grounding path.
1. For use with an electrical generator having a rotor with an electrically conductive rotor body, an insulated field winding wrapped around the rotor body, the field winding being connected to receive an exciter voltage at first and second exciter nodes, and a rotor grounding brush providing a grounding path between the rotor body and electrical ground, a system for detecting an open condition of the grounding path, the system comprising:
first and second buffer resistors coupled at a common node on one side of the first and second resistors, the opposite sides of the first and second resistors being coupled to respective one of the first and second exciter nodes;
a signal generator coupled to apply a periodic oscillating voltage signal to the common node;
a sense resistor coupling the signal generator to electrical ground;
a low-pass filter having an input coupled to receive a positive and a negative sense resistor voltage representative of a positive and negative voltage across the sense resistor, and having an output coupled to deliver a filtered positive sense resistor voltage signal and a filtered negative sense resistor voltage signal; and
a microcontroller coupled to the low pass filter and programmed to calculate a total capacitance between the insulated field winding and electrical ground to detect the open condition of the grounding path.
24. A method for detecting an open condition of a grounding path provided by a rotor grounding brush electrically connecting a rotor body of a rotor to electrical ground, the rotor including an insulated field winding wrapped around the rotor body and configured to generate a magnetic field upon receipt of an exciter voltage from a voltage exciter connected at first and second exciter nodes at respective upper and lower extremities of the insulated field winding, the method comprising:
applying a square wave voltage signal to a second end of each of a first and a second buffer resistor, a first end of each of the first and second buffer resistors operatively connected to respective first and second exciter nodes;
integrating a voltage sample of a plurality of voltage samples over one of a positive and a negative one-half period of the square wave voltage signal to form an integrated value, the plurality of voltage samples derived from one of a positive voltage and a negative voltage generated across a sense resistor operatively coupling a generator of the square wave voltage signal to electrical ground;
if the end of one of the positive and the negative one-half period of the square wave voltage signal has been reached and a value of an insulation resistance between the rotor body and the insulated field winding is substantially infinite, dividing the integrated value by a proportionality constant to calculate a total capacitance between the insulated field winding and electrical ground; and
declaring the open condition of the grounding path if the total capacitance is less than a pre-selected capacitance setting.
29. A computer readable storage medium having program code recorded thereon for detecting an open condition of a grounding path provided by a rotor grounding brush electrically connecting a rotor body of a rotor to electrical ground, the rotor including an insulated field winding wrapped around the rotor body and configured to generate a magnetic field upon receipt of an exciter voltage from a voltage exciter connected at first and second exciter nodes at respective upper and lower extremities of the insulated field winding, comprising;
a first program code encoded in computer-readable storage media for causing a square wave voltage signal to be generated and applied to a second end of a first and a second buffer resistor, a first end of each of the first and a second buffer resistors operatively connected to respective first and second exciter nodes;
a second program code encoded in computer-readable media for causing an interrupt at a predetermined time interval;
a third program code encoded in computer-readable storage media for measuring a value of one of a filtered negative sense resistor voltage signal and a filtered positive sense resistor voltage signal to form a voltage sample, the filtered negative sense resistor voltage signal derived from a negative voltage generated across a sense resistor operatively coupling the generator to electrical ground, the filtered positive sense resistor voltage signal derived from a positive voltage generated across the sense resistor;
a fourth program code encoded in computer-readable storage media for integrating the voltage sample over one of a negative one-half period and a positive one-half period of the square wave voltage signal to form a value of an integral of one of the corresponding filtered negative sense resistor voltage signal and the filtered positive sense resistor voltage signal;
a fifth program code encoded in computer-readable storage media for determining a value of an insulation resistance between the rotor body and the insulated field winding if an end of one of negative and the positive one-half period is reached;
a sixth program code encoded in computer-readable storage media for dividing the value of the integral of the one of the corresponding filtered negative sense resistor voltage signal and the filtered positive sense resistor voltage signal by a proportionality constant to calculate a total capacitance if the value of the insulation resistance is substantially infinite; and
a seventh program code encoded in computer-readable storage media for declaring the open condition of the grounding path if the total capacitance is less than a pre-selected capacitance setting.
2. The system of
where VRSP
4. The system of
5. The system of
(a) cause an interrupt at a predetermined time interval;
(b) measure a value of the filtered positive sense resistor voltage signal to form a voltage sample;
(c) integrate the voltage sample over a positive one-half period of the periodic oscillating voltage signal to form a value of an integral of the filtered positive sense resistor voltage signal;
(d) if an end of the positive one-half period is reached, determine a value of an insulation resistance RX between the electrically conductive body and the insulated field winding;
(e) if the value of the insulation resistance RX is infinite, divide the value of the integral of the filtered positive sense resistor voltage signal by a proportionality constant to calculate the total capacitance; and
(f) if the total capacitance is less than a pre-selected capacitance setting, declare the open condition of the grounding path, and reset the value of the integral to zero.
6. The system of
7. The system of
8. The system of
not declare the open condition of the grounding path if the total capacitance is not less than the pre-selected capacitance setting; and
reset the value of the integral to zero.
9. The system of
(a) cause an interrupt at a predetermined time interval;
(b) measure a value of the filtered negative sense resistor voltage signal to form a voltage sample;
(c) integrate the voltage sample over a negative one-half period of the periodic oscillating voltage signal to form a value of an integral of the filtered negative sense resistor voltage signal;
(d) if an end of the negative one-half period is reached, determine a value of an insulation resistance RX between the electrically conductive body and the insulated field winding;
(e) if the value of the insulation resistance RX is infinite, divide the value of the integral of the filtered negative sense resistor voltage signal by a proportionality constant to calculate the total capacitance; and
(f) if the total capacitance is less than a pre-selected capacitance setting, declare the open condition of the grounding path, and reset the value of the integral to zero.
10. The system of
11. The system of
12. The system of
not declare the open condition of the grounding path if the total capacitance is not less than the pre-selected capacitance setting; and
reset the value of the integral to zero.
13. The system of
14. The system of
16. The method of
comparing the total capacitance to a pre-selected capacitance setting if, at the end of a one-half period of the periodic oscillating voltage signal, a resistance value between the insulated field winding and the electrically conductive body is substantially infinite;
declaring the open condition of the grounding path if the total capacitance is less than the pre-selected capacitance setting; and
not declaring the open condition of the grounding path if the total capacitance is greater than the pre-selected capacitance setting.
17. The method of
during the one-half period, deriving a plurality of voltage samples from one of a positive voltage and a negative voltage generated across a sense resistor, the sense resistor operatively coupling a generator of the periodic oscillating voltage signal to electrical ground;
integrating a value of the plurality of voltage samples to form an integrated value; and
dividing the integrated value by a proportionality constant to calculate the total capacitance.
18. The method of
19. The method of
where VRSP
21. The method of
22. The method of
23. The method of
25. The method of
26. The method of
27. The method of
(a) causing an interrupt at a predetermined time interval;
(b) adding the voltage sample of the plurality of voltage samples to previous voltage samples of the plurality of voltage samples; and
(c) if the end of one of the positive and the negative one-half period has not been reached, repeating steps (a) to (c).
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None
The present invention generally relates to synchronous generators, and more specifically, to an apparatus and method for detecting a brush liftoff in a synchronous generator rotor circuit.
Synchronous electrical generators (“synchronous generators”) are used in electric utility systems to convert mechanical rotation (e.g., shaft rotation provided by a steam turbine) into alternating electric current via well-known electromagnetic principles. After suitable conditioning, the alternating electrical current is typically transmitted and distributed to a variety of power system loads.
In general, synchronous generator design is based on Faraday's law of electromagnetic induction and includes a rotating rotor driven by an external torque for inducing an electromagnetic field (EMF) in a stationary stator. The rotor includes a field winding wrapped around a rotor body, and the stator includes an armature winding wrapped around an armature body.
In operation, a direct current is made to flow in the field winding to generate a magnetic field. When the rotor is made to rotate, the magnetic field rotates with it, passing through the stator winding(s) and inducing an electric current therein.
Insulation material is utilized to cover the field winding(s) in order to electrically isolate the field winding(s) from the rotor body. As is known, detecting a loss of the insulation covering the field winding(s), or a field ground, is vital to ensuring reliable operation of the synchronous generator. While a field ground of insulation at one point along the field winding may be inconsequential to operation, field grounds at two locations along the field winding could result in serious damage to the synchronous generator.
One method used to achieve a field-ground protection is the so-called switched-DC injection method. One implementation of a switched-DC injection method is illustrated on page 61 of a Siemens AG instruction manual, entitled “Numerical Machine Protection 7UM515,” version v3.1, dated 1996, the complete disclosure thereof being incorporated herein by reference. A variation of the switched-DC injection method is also described in U.S. Pat. No. 6,794,879, entitled “Apparatus and Method for Detecting and Calculating Ground Fault Resistance,” issued on Sep. 24, 2004, naming Lawson et al. as inventors, the complete disclosure thereof being incorporated herein by reference. Unlike other switched-DC injection methods where a voltage is measured across a grounded “sense resistor” in order to determine a loss of field winding insulation, the '879 patent discloses using a voltage controlled oscillator (VCO) configured to measure a differential voltage across a floating sense resistor.
The switched-DC injection method requires that the rotor body be connected to electrical ground. This is typically accomplished by means of a (rotor) grounding brush. When the grounding brush no longer provides a low resistance circuit between the rotor body and electrical ground, “brush liftoff” has occurred, and the device performing the field-ground protection is no longer able to perform its task. Detecting such a brush liftoff, or open condition of the grounding path provided by the grounding brush, is therefore critical to reliable synchronous generator operation. The present invention provides such protection.
The invention is directed to a system and method for providing detection of a brush liftoff in a synchronous generator rotor circuit by monitoring and evaluating the capacitance between the field winding and electrical ground. A brush liftoff is declared when the monitored capacitance value undergoes a drastic reduction from its steady state capacitance value.
In accordance with one embodiment of the invention, a system for detecting brush liftoff in an electrical generator of the type which includes a rotor with an electrically conductive rotor body and an insulated field winding, the insulated field winding being wrapped around the rotor body and connected to receive an exciter voltage at first and second exciter nodes, and a rotor grounding brush electrically coupling the rotor body to electrical ground, includes first and second buffer resistors R each coupled at one end to a common node and at their opposite ends to respective ones of the first and second exciter nodes. The system further includes a signal generator coupled to apply a periodic oscillating voltage signal to the common node, a sense resistor RS coupling the signal generator to electrical ground, and a low-pass filter. The input of the low-pass filter is coupled across the sense resistor to receive positive and a negative sense resistor voltages VRSP and VRSN. The low-pass filter develops a filtered positive sense resistor voltage signal VRSP
In accordance with another embodiment of the invention, a method for detecting an open condition of a grounding circuit provided by a rotor grounding brush electrically connecting an electrically conductive body of a rotor to electrical ground includes a rotor having an insulated field winding wrapped around the electrically conductive body where the insulated field winding is coupled to receive an exciter voltage at first and second exciter nodes, includes applying a periodic oscillating voltage signal to a common node between first and second buffer resistors, coupling the exciter voltage to the first and second buffer resistors, calculating a total capacitance CFG between the insulated field winding and electrical ground, and determining from the total capacitance whether an open condition exists in the grounding circuit.
In accordance with a further embodiment of the invention, a method for detecting an open condition of a grounding circuit provided by a rotor grounding brush electrically connecting a rotor body of a rotor to electrical ground, wherein the rotor has an insulated field winding wrapped around the rotor body and the insulated field winding is configured to generate a magnetic field upon receipt of an exciter voltage from a voltage exciter connected at first and second exciter nodes at respective upper and lower extremities of the insulated field winding, includes applying a square wave voltage signal to a second end of each of a first and a second buffer resistor. A first end of each of the first and second buffer resistors is operatively connected to respective first and second exciter nodes. The method further includes integrating a voltage sample of a plurality of voltage samples over one of a positive and a negative one-half period of the square wave voltage signal to form an integrated value, and dividing the integrated value by a proportionality constant to calculate a total capacitance CFG between the insulated field winding and electrical ground, and declaring the open condition of the grounding path if the total capacitance is less than a pre-selected capacitance setting.
It should be understood that the present invention includes a number of different aspects and/or features which may have utility alone and/or in combination with other aspects or features. Accordingly, this summary is not an exhaustive identification of each such aspect or feature that is now or may hereafter be claimed, but represents an overview of certain aspects of the present invention to assist in understanding the more detailed description of preferred embodiments that follows. The scope of the invention is not limited to the specific embodiments described below, but is set forth in the claims now or hereafter filed.
Although the characteristic features of this invention will be particularly pointed out in the claims, the invention itself, and the manner in which it can be made and used, can be better understood by referring to the following description taken in connection with the accompanying drawings forming a part hereof, wherein like reference numerals refer to like parts throughout the several views and in which:
Referring to the Drawings, and particularly to
To detect grounding of the field winding 158 a square wave voltage signal 164 is applied to first and second exciter nodes 161 and 163 on the field winding via buffer resistors R166. Signal 164 has a frequency FDC and provides positive and negative injected DC voltages VDCP 167 and VDCN 169, respectively (i.e., injected switched-DC current). The period TDC of signal 164 corresponds to switching frequency FDC, and therefore during the period TDC, each of the positive and negative injected DC voltages VDCP and VDCN are applied to respective exciter nodes 161, 163 during an interval equal to one-half of the period TDC or TDC/2 186. As illustrated, a low pass filter 171 is also included in the synchronous generator rotor assembly 150 to provide electrical noise abatement.
The synchronous generator rotor assembly 150 has a resistance RX between rotor body 152 and field winding 158; a resistance RS between a circuit node receiving the square wave voltage signal 164 and electrical ground 154; and a capacitance CFR between field winding 158 and rotor body 152. Under normal conditions (i.e., no brush liftoff), a capacitance value represented by the field capacitor CFR 174 is equal to the capacitance between field winding 158 and electrical ground 154.
Referring to the electrical equivalent circuit of
Conversely, if insulation resistor RX 170 has a value indicating a loss of field winding insulation, a significant voltage will develop across sense resistor RS 172 upon application of signal 164 as DC current will flow. In that case, at the end of the positive half-period of signal 164, a positive sense resistor voltage VRSP 165a develops across the sense resistor RS 172. Similarly, at the end of the negative half-period of signal 164, a negative sense resistor voltage VRSN 165b develops across sense resistor RS 172. The magnitude of both of the filtered positive sense resistor voltage signal VRSP
For ease of discussion, the following variables may be defined where:
Referring again to
Alternatively, if the value of excitation voltage VFDP 160a at the end of the positive half-cycle and excitation voltage VFDN 160b at the end of the negative half-cycle are not assumed to be equal, the insulation resistance can be computed using Equation (2), taking into account the change into the excitation voltage:
Equation (2) may be expressed otherwise by introducing the distance to the fault x (varying between 0 and 1) as a variable:
Equations (1) through (3) assume that the electrical equivalent circuit of
The nature of such a transient voltage may be represented by
When the positive injected DC voltage VDCP 167 is first applied to the switched-DC portion of rotor assembly 150, the transient voltage across the sense resistor RS 172 will be an exponentially decaying waveform. For example,
where VRSpeak corresponds to the highest value of the exponentially decaying transient waveform that begins at the start of each one-half period TDC/2 186, and where a first time constant τFIRST, or a pre-brush liftoff time constant, is equal to:
τFIRST=(R+RS)*CFR (5)
Referring to Equation (3), field capacitor CFR 174 is representative of the capacitance between field winding 158 and the rotor body 152. Because rotor body 152 is connected to electrical ground 154 via grounding brush 156, however, the capacitance value represented by field capacitor CFR 174 is also equal to the capacitance between field winding 158 and electrical ground 154.
The voltage across sense resistor RS 172 will also be a negative transient waveform 187 when the negative injected DC voltage VDCN 169 is applied to the electrical equivalent circuit of the switched-DC portion of rotor assembly 150. It should be noted that the voltage across sense resistor RS 172 is assumed to go to zero in a steady state. A zero voltage across sense resistor RS 172 corresponds to the situation where the insulation resistor RX 170 has very high value close to infinity and is therefore properly isolating field winding 158 from the electrical ground 154.
Because rotor body 152 is now connected to electrical ground 154 via capacitor CRG 192, due to the brush liftoff condition, a second time constant τSECOND, or a post-brush liftoff time constant, may be defined as:
where the capacitance value represented by capacitor CFG 194 is much smaller than the pre-brush liftoff capacitance value represented by field capacitor CFR 174. As a result, the post-brush liftoff time constant τSECOND will be much smaller than the pre-brush liftoff time constant τFIRST. Accordingly, an exponentially decaying transient signal will decay more quickly and the voltage across sense resistor RS 172 will settle to its steady state final value of zero much more rapidly.
In accordance with the invention, the filtered positive and negative sense resistor voltage signals 102 and 103 in a transient-state are used to determine an occurrence of a brush liftoff condition. More specifically, the positive and negative voltage signals across sense resistor RS 172 are processed through low-pass filter 171 to form the filtered positive sense resistor voltage signal VRSP
The microprocessor 112, executing a computer program or voltage control logic scheme (discussed below in connection with
As shown by
Upon each interrupt, the microcontroller 110 measures either the filtered positive sense resistor voltage signal VRSP
Next, the microcontroller 110 integrates using the voltage samples measured from the filtered positive sense resistor voltage signal VRSP
An exponentially decaying transient waveform results upon initial application of either the positive injected DC voltage VDCP 167 portion or the negative injected DC voltage VDCN 169 portion of the square wave. Further, as demonstrated above in Equation (4), the value of the voltage across the sense resistor RS 172 after application of the positive injected DC voltage VDCP 167 is
where VRSPEAK is the highest value of the exponentially decaying transient waveform. For purposes of the insulation resistance Rx calculation, in order to effectively measure the final value of the positive sense resistor voltage VRSP 165a, it is necessary to wait until a value of its exponentially decaying transient waveform has become negligible. A square wave switching frequency FDC must therefore be selected to ensure that the last voltage sample measured from the filtered positive sense resistor voltage signal VRSP
To accomplish the last transient free voltage sample, the switching frequency FDC of the square wave signal 164 is selected so that the one-half period TDC/2 186 is a multiple of the longest expected time constants. For example, if the one-half period TDC/2 186 is selected to be five times the time constant τ, a value of the exponentially decaying transient waveform decreases to a level within 1% of the steady state or its final value at the end of expiration of the one-half period TDC/2 186.
Integrating the positive sense resistor voltage VRSP 165a over the one-half period TDC/2 186 yields:
Substituting the value of the pre-brush liftoff time constant τFIRST=(R+RS)*CFR in the integral of the positive sense resistor voltage VRSP 165a yields a pre-brush liftoff integral:
integral[VRSP]FIRST=VRSPEAK(R+RS)*CFR (8)
where VRSPEAK R and RS are constants having values fixed by the circuit design. A pre-LPF proportionality constant KC1 can be introduced in the Equation (6) such that the integral of the positive sense resistor voltage VRSP 165a is proportional to the capacitance value represented by the field capacitor CFR:
integral[VRSP]FIRST=|integral[VRSN]|=KC1CFR (9)
Equation (9) also illustrates that the absolute value of the integral of the negative sense resistor voltage VRSN 165b is equal to the integral of the positive sense resistor voltage VRSP 165a.
As described in connection with Equation (6), the post-brush liftoff time constant τSECOND may be expressed as
Thus the integral of the positive sense resistor voltage VRSP 165a over the one-half period TDC/2 during the brush liftoff condition may be expressed as:
As described in connection with
Referring to
In operation, first integration is performed by the first integration block 306 by summing exponentially decaying transient waveform samples taken at a rate of 1 kHz (one sample every millisecond). The first integration yields an integrated transient waveform 307. The exponentially decaying transient waveform is also processed through the low-pass filter 308 and then integrated via the second integration block 310 to form the integrated filtered transient waveform 311.
The results of the first and second integrations are listed in Table 1:
TABLE 1
Time-
Capacity
1/Time-
Integration I
Integration II
Constant (s)
(microF)
Constant
(307)
(311)
0.375
10
2.666666667
373.67
373.07
0.28125
7.5
3.555555556
281.52
281.02
0.1875
5
5.333333333
188
187.52
0.09375
2.5
10.66666667
94.25
93.77
0.0375
1
26.66666667
38
37.52
0.028125
0.75
35.55555556
28.63
28.15
0.01875
0.5
53.33333333
19.25
18.77
0.009375
0.25
106.6666667
9.88
9.4
0.00375
0.1
266.6666667
4.27
3.77
0.0028125
0.075
355.5555556
3.34
2.84
0.001875
0.05
533.3333333
2.42
1.9
0.0009375
0.025
1066.666667
1.52
0.963
0.000375
0.01
2666.666667
1.07
0.4
For further illustration,
Based on the above analysis and Equations (9) and (10), the integrals of the pre- and post-brush liftoff filtered positive sense resistor voltage signal VRSP
Replacement of the pre-LPF proportionality constant KC1 with the post-LPF proportionality constant KC2confirms the small change between the constants of proportionality when the instantaneous voltage across the sense resistor RS 172 is measured at the output of the low-pass filter rather than at the input.
Referring again to
As discussed in connection with
Assuming that the pre-LPF and post-LPF proportionality constants KC1 and KC2 are determined experimentally, Equations (13) and (14) provide a basis for computing the capacitance between the field winding 158 and the electrical ground 154 (i.e., a capacitance value represented by the total capacitor 194):
Because the voltage samples used for the integration step 206 are based on the filtered positive sense resistor voltage signal VRSP
Referring again to
Upon a determination of whether a brush liftoff has occurred during the half-period TDC/2 186 in which the filtered positive sense resistor voltage signal VRSP
The present method may be implemented as a computer process, a computing system or as an article of manufacture such as a computer program product or computer readable medium. The computer program product may be a computer storage media readable by a computer system and encoding a computer program of instructions for executing a computer process. The computer program product may also be a propagated signal on a carrier readable by a computing system and encoding a computer program of instructions for executing a computer process.
In one embodiment, the logical operations of the present method are implemented (1) as a sequence of computer implemented acts or program modules running on a computing system and/or (2) as interconnected machine logic circuits or circuit modules within the computing system. The implementation is a matter of choice dependent on the performance requirements of the computing system implementing the invention. Accordingly, the logical operations making up the embodiments of the present invention described herein are referred to variously as operations, structural devices, acts or modules. It will be recognized by persons skilled in the art that these operations, structural devices, acts and modules may be implemented in software, in firmware, in special purpose digital logic, and any combination thereof without deviating from the spirit and scope of the present invention as recited within the claims attached hereto.
While this invention has been described with reference to certain illustrative aspects, it will be understood that this description shall not be construed in a limiting sense. Rather, various changes and modifications can be made to the illustrative embodiments without departing from the true spirit, central characteristics and scope of the invention, including those combinations of features that are individually disclosed or claimed herein. Furthermore, it will be appreciated that any such changes and modifications will be recognized by those skilled in the art as an equivalent to one or more elements of the following claims, and shall be covered by such claims to the fullest extent permitted by law.
Benmouyal, Gabriel, Nguyen, Thanh-Xuan Thi
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